Legalities of children born out of wedlock

It's quite complicated. You will need a legal document from your child's father giving you full custody of your child.

Custody or responsibility

Thank you
My fiance and I are now married,
but his company has said they cannot assist with my daughter as there is no father on her birth certificate

That poses a problem.  You have two options:

1) If the father is not listed on the birth certificate; in most countries, they can sign a "paternity acknowledgement" at a later stage to get themselves added to the birth certificate and a new copy is issued.  Different countries have different rules for this
2) You need to consult a lawyer and figure out how you can add your fiance as a legal guardian / father for your daughter and ask your company to check if that would be acceptable.  Keep in mind that this option has potential issues:
a) You will be asked if the Father is "unknown".  If so, it may or may not be accepted and you might be asked to provide hospital records.  Does pose reputational risks to yourself in this part of the world which is extremely conservative
b) If the father is "known" then it is likely to be redirected to option #1 and in addition, get the consent / custody documents from the father for the daughter

Thank you, I believe I have to get my country to issue a new birth cert with the fathers details and also include a legal letter saying he will give permission for my daughter to travel with me

Correct. That is the easiest solution.

Refer to this link: http://lmra.bh/portal/en/page/show/189

You need a no objection certificate as well as a statement proving your custody of your daughter.